T S M M ( s n o it a c il p p A d n a s e i g o l o n h c e T n o it a l u m i S d n a g n il l e d o M , s c it a m e h t a M n o e c n e r e f n o C l a n o it a n r e t n I 7 1 0
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u o h z n a L , g n i r e e n i g n E d n a e c n e i c S n o it a m r o f n I f o l o o h c
S Universtiy,Lanzhou,China r o h t u a g n i d n o p s e r r o C * : s d r o w y e
K COMSOL Mulitphysics, Surface Enhanced Raman Scattering, locailzed surface e c n a n o s e r n o m s a l
p , hotspots.
.t c a r t s b
A A simplenanospheredimersystem wasconstructedbased on thewaveopticsmodule in s c i s y h p i t l u M L O S M O
C toverifyt heirho tspotseffect .Bymappingt heirelectricfielddistributions, we found tha tas the nanogap decreases or the nanosphere radius increases in a way ,the field
r e m i d e h t f o t n e m e c n a h n
e goes up .In addtiion ,the resonan tpeak along with the excitation o s l a n a c h t g n e l e v a
w be tuned by varying the size and nanogap of the nanospheres. We have t a h t d e t a r t s n o m e
d the strong interaction between two nanospheres may be induced by the dipole , g n i l p u o
c consisten twithourcurrentlyacceptedtheory.Theresultsshowed ticouldbeausefu ltoo l t a l u m i s d n a n g i s e d e r u t u f r o
f i on of electromagnetic fields and electromagnetic waves correlated s e l c it r a p o n a n h t i w . n o it c u d o r t n I t n e m p o l e v e d e h t g n i y n a p m o c c
A o f Surface-enhanced Raman scattering (SERS)[ , t1] i has d e s u o r
a tremendous interest of researchers from al lover the world due to tis good application t c e p s o r
p .SERS sh a no tonlyhighsensitivity ,bu talsolowinterferenceandhighstabiltiy .Therefore , d e h t e z i l a e r n a c e
w etectionofsinglemolecularl evel[ - ]2 4 byprovidingvibrationi nformationoft he e l u c e l o m t e g r a
t . Therefore ,i tis now widely used as a spectroscop ic method to identificaiton and t
c e t e
d i on ofbiologica land chemica lsamples[5 ,6]. Compare d with theordinary Raman scattering , s l a n g i
s SERSsignalscan amplify theRaman scattering signa l109- 01 12 itmesby localized surface e c n a n o s e r n o m s a l
p (LSPR)[7]of metall ic nanoparticle .The LSPR i s charge denstiy oscillations o t d e n i f n o
c metall ic nanoparticles (sometimes referred ot as meta l clusters) and metall ic s e r u t c u r t s o n a
n [8] .I toccurs in metallic nanostructures such asnanoparticles[ ,9] nanocylinders[10], o
n a
n islands[11]. tI is an interaction between the metal nanoparticles and the light liluminated on e
h
t m O. nce the frequency of the inciden tligh tis equa lto the oscillation frequency of the metal e l c i t r a p o n a
n ,the resonance occurs which shows macroscopically the absorption of ligh tby the . s e l c i t r a p o n a n c i l l a t e m s
A isreferencedabove,theexcitationof LSPRi ninfraredorvisiblel ightoft hespectruml eadst o a prominent enhancemen t of the electric field generated in the adjacen t area of the meta l
e l c i t r a p o n a
n relative to the inciden telectric fie ld. In genera,l the gold and silver show the mos t t n a c i f i n g i
s enhancemen teffect .Although various nanoparticle geometries have been efficiently d e t a c i r b a f d n a d e s i v e
d ,oneofthemos tsimplebu tplasmonically momentousstructures stil listhe p a g o n a n a y b d e t a r a p e s ) s P N ( s e r e h p s o n a n c i l l a t e m o w t f o g n i t s i s n o c , r e m i
d [12 ,13]. Researchers
e v e i l e b y l l a r e n e
g d tha ttheintenseelectromagneticfieldenhancemen tappearsin thisnanoscalegap e h t o t e u
d LSPR coupilng effect, and the field distribution generated in the nanogap is very e h t f o e g n a h c e h t o t e v i t i s n e
s dimensiona lparametersofthe coupling system which composed of c i l l a t e
m nanospheredimer, theso-calledho tspots[14 ,15]. e s o o h c e w , k r o w s i h t n
I silver nanophere dimer a tnorma lincidence, aiming to summarize its r
a e
n -field enhancemen tand resonance shifts .With the frequency-domain finite elemen tmethod )
M E F
( ,wesystematically analyze thewavelength-dependen tnear-field distribution by varying the s
u i d a
r andnanoscalegap width oftheNPs dimerinthiscoupling system. Thesysteminvestigated r e p a p s i h t n
, s c i t p
o and provide a genera lmethod and indicaiton of the related near-field enhancemen tof s
P N c i l l a t e
m .
d n a s l e d o
M Principle
Electrodynamic simulations are performed using FEM with a commercia l software package (COMSOL Multiphysics 5.2a) ,is an authenitcally arbitrary multi-physics field direc tcoupling
, e r a w t f o s s i s y l a n
a i sappropriateforsimulationofvariousphysica lprocessesinthefieldofscience g
n i r e e n i g n e d n
a .COMSOL Multiphysicsoffersalargequanitty ofpredefined physica lapplication e
l u d o
m , covering acousitcs ,electrochemistry ,hea ttransfer ,wave optics ,RF module ,etc. In this e
w , t r o p e
r are going to introduce the wave optics module which has been widely used to d
e r p , d n a t s r e d n
u ic tanddesignresonanceeffect intransmissionofelectromagneticwaveandoptica l n
o it a c i l p p
a byengineers.Thismodules includeelectromagneticfieldsandelectromagneticwavesi n o
w
t -dimensiona land three-dimensiona lspace .Al lsimulation formulas are based on Maxwel l s
n o it a u q
e [16] and combining the laws of materials used for transmission in a variety of media. ,
e c a f r e t n i s c i s y h p d e n i f e d e r p e h t h g u o r h
T tha tiswa veopitcsinterface ,includingthesimulation of f
c i t e n g a m o r t c e l e e h
t ields and waves in the frequency domain , itme domain ,eigenfrequency and s
i s y l a n a e d o
m so thattheusers canestablish andsolvetheelectromagneticfield mode.lInaddiiton e
h t o t n i d e d i v i d s i d n a e s i c n o c y r e v o s l a s i e l u d o m s i h t f o w o l f k r o w e h t , s i h t o
t following steps :
a g n i s o o h c , s l a i r e t a m g n i s o o h c , y r t e m o e g g n i n i f e
d ppropriate wave optics interfaces , defining v
d n a s r e v l o s g n i t c e l e s , s e h s e m t n e m e l e e t i n i f g n i n i f e d , s n o i t i d n o c l a i t i n i d n a s e i r a d n u o
b isuailzing
.t l u s e r
a c i p y
T lly ,Fig .1 shows the simulation mode,l tha tis the structure consists of Ag NPs. In the ,
n o i t a l u m i
s wave optics-electromagnetic wave ,frequency domain(ewfd) module was applied , et h o
t ) L M P ( r e y a l d e h c t a m y l t c e f r e p a y b d e t a c n u r t s a w n i a m o d n o i t a t u p m o
c simulate a situation in
e h t e v o b a r i a e h t h c i h
w NPswerei nfinitetoavoidunphysica lreflectionsaroundt heNPs. Inviewof ,
n o it a c i l p p a l a c i t c a r p e h
t fort heexcitationbeam ,weusel inearlypolarized ilgh,tt hedirecitonoft he e
v a w t n e d i c n
i -vector k is perpendicular to the dimer axis ,w tih the polarization is paralle lto the g
n i t c e n n o
c axis fo dimer(seei nse tinFig .1). Differen tmeshunitshavebeencheckedtoehancet he d
n a y t i l i b a i l e
r savethe computation memory and calculation time. Theoptica lconstantsofsilver e
h t m o r f n e k a t e r e w r i a d n
a materiall ibrary.
g i
F u 1 .re Dimerstructurecomposedoft woAgnanosphereswith20nmradiusand5nmnanogap.
Resutls da Dn sicus ison
o t g n i d r o c c
A SERStheory[17] ,theSERSenhancemen tfactor(EF)wasassumedto beproportiona l o
t |𝐸𝑙/𝐸0|4 ,where 𝐸𝑙 and 𝐸0=1V/m are the amplitudes of the localized electric fields and t
n e d i c n
i fields ,respecitvely. Asageneralmatter ,changing theparameters ofnanostructuresin the l
l i w s t o p s t o h f o n o i t u b i r t s i d e h t , e g n a r h t g n e l e v a w n o i t a t i c x e e t a i r p o r p p
a present acorresponding
. e g n a h
c Takingi ntoaccoun tthevibrationabsorptionpeakofsilver[18] , ew firsltyincreasenanogap h
t d i
w d from 3 to 20 nm and keeping radius r=20nm unchanged with given various excitation s
h t g n e l e v a
w ,as shown in Figure .2(a). We can see tha t as the nanogap increases ,the field n
e e w t e b t n e m e c n a h n
e u l
b shif.tTheresonancepeakshiftismainlyonaccoun tofthedipole-dipoleinteraction .Duet othe s
n o r t c e l e a m s a l p e h t f o t n e m e n i f n o
c ofa single nanosphere ,the surface charges generated by the d
e t a i d a r r
i ligh twil lbear repulsive forces. However ,as another nanosphere approaches it ,t he s
e r e h p s o n a n h t o b n o t c a s e c r o f l a n o i t i d d a n o i t a z i r a l o
p .A tthis point ,the repulsive force in each d
e n e k a e w s i e r e h p s o n a
n yb the attractive forces between the charge distribution of two e
r e h p s o n a
n s ,resulting in acorrespondingly higher resonance wavelength[19]. Figure. 2(b) shows x
t a n o i t u b i r t s i d d l e i f e h
t -zcrosssection .Wecan clearlyobservetha tthesmallerthegap between e
s n e d e r o m e h t , s e r e h p s o n a n e h
t of the field distribution, accordingly ,the greater the maximum .t
n e m e c n a h n e d l e i f
e r u g i
F . 3(a) plotstheenhancemen tspectrum representsthe maximum field enhancementin the m
n
5 gap region of nanosphere dimerswith differen tradius. Asshown in Figure. 3 ,the ho tspots .
s u i d a r e r e h p s o n a n e h t o t l a n o i t r o p o r p y l t c e r i d t o n s i t c e f f
e The SERS intensity increaseswith the e
r e h p s o n a n e h t f o e s a e r c n
i radiusandthenlevelsoff .Asexpected ,thereasonancepeakwavelength t
f i h
s s from 380 nmto 410 nm as thenanosphereradiusfrom 10 nm to 52 n Tm. o someextent ,a e
r u t c u r t s r e m i d e r i t n e e h t f o g n i p m a d n o it a i d a r r e t a e r g e h t t a h t n a e m o s l a y a m s u i d a r r e g r a
l [20 ,21] .
g i
F u .re2 (a)Simulatedelectricfieldi nnanogapofAgdimera tvariouswavelength .(b)Typicall oca lelectricfield s
n o i t u b i r t s i
g i
F u .re3 (a)Simulatedelectricfieldi nnanogapofAgdimera tvariouswavelength .(b)Typicall oca lelectric s
n o i t u b i r t s i d d l e i
f o ndifferen tnanosphereradiusr.
, n o i s u l c n o c n
I dueto theLSPReffect ,thestronginteractionbetweentwonanospheresisinduced e
l o p i d e h t y
b coupling through the modeling analysis ,leading to an enhancemen tof the electric .
y t i s n e t n i d l e i
f Therefore ,increasing the nanosphere radius within a certain range while the two y
l t a e r g n a c , r e h t e g o t e s o l c e r a s e r e h p s o n a
n augment the “ th -o spots” effect. This conclusion is e
s u o s l a e W . h c r a e s e r s u o i v e r p e h t h t i w t n e t s i s n o
c thewaveopticsmodule ofCOMSOLto analyze c
i r t c e l e e h t f o e c n e d n e p e d e h
t fieldontheexcitaiton wavelength .In short ,thismodulealso can be o
t d e s
u optica lmetamaterials design ,waveguides ,and couplers analyses ,and nonlinear optics c
t e n g i s e
d . ,providinggrea thelpf mor u tliphysicsfieldcouplinganalysis.
t n e m e g d e l w o n k c A
s a w h c r a e s e r s i h
T funded by 2017 teaching researchprojec tofLanzhou University (gran tnumbers .
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